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Performance analysis of reset control systems
Author(s) -
Aangenent W. H. T. M.,
Witvoet G.,
Heemels W. P. M. H.,
van de Molengraft M. J. G.,
Steinbuch M.
Publication year - 2010
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1502
Subject(s) - reset (finance) , control theory (sociology) , convex optimization , simple (philosophy) , norm (philosophy) , nonlinear system , controller (irrigation) , mathematics , quadratic equation , linear matrix inequality , piecewise , lyapunov function , computer science , mathematical optimization , regular polygon , control (management) , philosophy , artificial intelligence , law , mathematical analysis , financial economics , biology , geometry , epistemology , quantum mechanics , political science , agronomy , physics , economics
In this paper we present a general linear matrix inequality‐based analysis method to determine the performance of a SISO reset control system in both the ℒ 2 gain and ℋ 2 sense. In particular, we derive convex optimization problems in terms of LMIs to compute an upperbound on the ℒ 2 gain performance and the ℋ 2 norm, using dissipativity theory with piecewise quadratic Lyapunov functions. The results are applicable to for all LTI plants and linear‐based reset controllers, thereby generalizing the available results in the literature. Furthermore, we provide simple though convincing examples to illustrate the accuracy of our proposed ℒ 2 gain and ℋ 2 norm calculations and show that, for an input constrained ℋ 2 problem, reset control can outperform a linear controller designed by a common nonlinear optimization method. Copyright © 2009 John Wiley & Sons, Ltd.